Often, fluency in arithmetic is understood to mean that students can use the standard American algorithms to achieve correct answers quickly. Unfortunately, simply mastering the steps of the standard American algorithms does not ensure that students have a deep understanding of the concepts of multi-digit addition and subtraction. The standards in this strand allow students to build conceptual understandings in a variety of ways prior to learning and mastering the standard American algorithms. While the expectation for learning this algorithm remains, the standards in this progression allow students to understand why the algorithms work by first constructing concrete understandings, moving to strategies that connect to understandings of place value and the properties of operations, and then to mastering the standard American algorithms.
